You won't have any issue at all with the clients reporting into the upgrade core server. You should look to upgrade the clients as soon as is feasible as in v9, there have been a lot of changes around how software licensing works and you won't have it working properly without the new agent. Standard Hardware and Software inventory should be fine though.

The 8.8 clients will continue to work with the 9.0 core as long as you copy over the certificates from the 8.8 core. Since you are going to use the same name that will remove having to create a DNS alias for your core. If you are going to use coredatamigration.exe, that will copy over most of the settings as well as the certs. Info on how to use it can be found here http://community.landesk.com/support/docs/DOC-6970